Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

Kuroiwa, Kohdai; Takagi, Ryuji; Adesso, Gerardo; Yamasaki, Hayata

doi:10.1103/physreva.109.042403

Phys. Rev. A

2024

DOI: 10.1103/physreva.109.042403

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Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

Kohdai Kuroiwa,

Ryuji Takagi,

Gerardo Adesso

et al.

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Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity

Kuroiwa,

Takagi,

Adesso

et al. 2024

Phys. Rev. Lett.

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Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. Quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a non-convex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a non-linear resource witness and reveal that any state is more advantageous than a free one in some multi-copy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states.

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Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity

Kuroiwa,

Takagi,

Adesso

et al. 2024

Phys. Rev. Lett.

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Robustness- and weight-based resource measures without convexity restriction: Multicopy witness and operational advantage in static and dynamical quantum resource theories

Cited by 1 publication

References 106 publications

Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity

Every Quantum Helps: Operational Advantage of Quantum Resources beyond Convexity

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